All electro-magnetic radiation has a polarization vector associated with it. This vector is a complex two-dimensional spatial vector. The vector is contained within a plane that is perpendicular to the direction of propagation of the electric field. Within this plane, however, the vector may have any orientation. The complex nature of the vector stems from the fact that the orientation and magnitude of the vector may change with time, sweeping out an ellipse. Spatial phase vectors are present across the entire EM spectrum as well as for emitted, reflected and transmitted radiation and the devices to be described herein need not be limited to a single region of the spectrum.
The spatial phase of EM radiation emanating from the surface of an object, whether it is emitted, transmitted, or reflected, has a measurable spatial phase. Thus the shape of the object, the type of material from which it is made, the orientation of the object relative to the observer, etc., all effect the spatial phase of EM radiation emanating from the object. As a result, the various objects within a scene will each have a distinct spatial phase signature.
Most detection systems, especially imaging systems, measure the amplitude of the emitted EM radiation while ignoring the spatial phase of this radiation. However, there is inherently more information contained within the spatial phase than in the amplitude alone and sensors which can measure the spatial phase vector will have greater detection and discrimination capability than those which simply measure the amplitude. Illustrating this point is the fact that the amplitude information can be derived from the spatial phase data. The converse is not true.
Measuring the spatial phase of a light beam requires several optical elements in addition to those required for amplitude detection. These additional elements include but are not limited to polarizers and retarder plates. These two elements are complimentary and when used together can accurately measure the spatial phase of light incident on them.
Polarizers transmit a fixed spatial phase state independent of the incident spatial phase, in effect, filtering the incident light. Although the spatial phase of the transmitted light is independent of the incident spatial phase, the intensity of the transmitted radiation does depend on the incident state. A retarder, on the other hand, modifies the spatial phase but does not perform any filtering functions. The spatial phase transmitted by a retarder is dependent on the spatial phase of the incident light while the transmitted intensity is independent of the spatial phase of the incident radiation.
Quantitative analysis of the spatial phase of a light beam requires a mathematical formalism for describing the polarization state of radiation and the polarization altering properties of polarization elements. The principal computational methods for treating polarization problems are the Stokes elements, Jones calculus and the Mueller calculus.
The polarization state of radiation is described by the Stokes vector, a four element real vector: ##EQU1## where the lower case letters represent elements normalized by the first element of the vector S.sub.0. The units of the Stokes vector are intensity. The first element of the Stokes vector S.sub.0 gives the intensity of the radiation and is the only element that is directly measurable by experiment. The other three elements of the Stokes vector S.sub.1, S.sub.2 and S.sub.3 describe the polarization state of the radiation and give the "preference" for horizontal, .+-.45.degree., and right/left circular polarized radiation.
Formally, the S.sub.1 element represents the difference in intensities for horizontally and vertically polarized radiation, the S.sub.2 element is the difference in intensities for radiation polarized along the .+-.45.degree. axes, and S.sub.3 is the difference of right/left circularly polarized radiation. For the normalized Stokes vector, the elements range from 1 to -1. The S.sub.1 element takes on a value of 1 for completely horizontally polarized radiation and is -1 for completely vertically polarized radiation. Similarly, the S.sub.2 element is 1 and -1 for .+-.45.degree. and -45.degree. polarized radiation, and S.sub.3 =1 represents right circular radiation and S.sub.3 =-1 is left circular. The degree of polarization is found from: EQU DOP=S.sub.1 +S.sub.2 +S.sub.2 /S.sub.0 EQU DOLP=S.sub.1 +S.sub.2 /S.sub.0 ( 2) EQU DOCP=.vertline.S.sub.3 .vertline./S.sub.0
where DOP is the degree of polarization including linear and circular polarization, DOLP is the degree of linear polarization, and DOCP is the degree of circular polarization. DOP=1 represents totally polarized radiation, DOLP=1 represents totally linear polarized radiation, and DOCP=1 is totally circularly polarized radiation.
Additional polarization vector metrics that may be obtained from the Stokes vectors are ##EQU2## where DOUP is the degree to which the light is unpolarized, .THETA. is the orientation of the major axis of the polarization vector, and ellipticity is a measure of the relative magnitude of the major and minor axes. The spatial phase of radiation is defined by the complete set of polarization metrics.
Devices which measure the spatial phase of the EM radiation which is incident on them are referred to as polarimeters or polarization state analyzers. Conventional polarimeters measure the area average of the spatial phase for a beam of light. Variations of the spatial phase from point to point within the beam are averaged. An imaging polarimeter is a special class of devices in which the variations of the spatial phase from point to point within a beam of light (or equivalently from point to point within a scene or across an object) are measured. A two dimensional array of detectors is used for this device instead of a single detector as used in conventional polarimetry.
The spatial phase cannot be measured directly but may be calculated from a set of complimentary intensity measurements. There are numerous measurement sets from which the spatial phase may be calculated, each of which requiring a separate calculation method. For clarity, the methods described herein will first calculate the Stoke's vectors and then the polarization metrics. The Stoke's vectors are intermediary and need not necessarily be calculated.
Two approaches for obtaining the Stokes vector are described below. For consistency the approaches will be described for an imaging polarimetry system as disclosed herein.
The first approach for obtaining a set of complimentary intensity measurements includes the use of a sensor such as a focal plane array, an imaging lens, a 1/4-waveplate, and a polarizer, as discussed in detail hereinbelow. The waveplate is placed in front of the polarizer. The waveplate/polarizer combination may be placed either in front of the lens or between the lens and the sensor. An image is acquired at a finite number of regularly spaced angular positions of the waveplate (for example 16). The 16 intensity measurements for a given pixel (corresponding to a single object point) will sweep out a curve as a function of the angular position of the waveplate.
This curve is characteristic of the spatial phase of the radiation for that object point and may be analyzed to determine the Stokes parameters as well as a number of other polarization metrics. This analysis may be performed in two ways (1) using a measurement matrix and (2) performing a Fast Fourier Transform (FFT) on the data and making a few calculations. The FFT method is outlined below.
Linear polarized light produces a signal that has four maxima and minima and will appear in the fourth harmonic component of the FFT data. The orientation of the linearly polarized signal determines the phase of the fourth harmonic component as well as contributes to the DC component. Circularly polarized produces two maxima and minima and will appear in the second harmonic component of the FFT data. The handedness (i.e. clockwise rotation or counter clockwise rotations) determines the phase of the second harmonic component. Unpolarized light produces a DC signal that appears in the DC component of the FFT data. The relative amplitudes of these components determine the degree to which the light is linear polarized circularly polarized, etc.
These effects can be quantitatively determined from the following equations. The parameters of the Stokes vector are obtained using ##EQU3## where A.sub.0 and A.sub.4 are the real parts of the DC and fourth harmonic components respectively and B.sub.2 and B.sub.4 are the imaginary components of the second and fourth harmonic components. It should be noted that the polarization metrics can be calculated directly from the FFT data without calculating the intermediate Stokes vectors.
The second approach for obtaining a set of complimentary images is to measure the intensity emitted (or reflected) from an object through a series of four filters. The choice of the filters is not unique. One particularly intuitive and insightful set of filters is (1) a polarizer at 0.degree., (2) a polarizer at 45.degree., (3) a quarter wave retarder (or equivalently a 1/4 .lambda. wave-plate which converts circular polarized light into linear polarized light) and polarizer, and (4) a 50% transmitting neutral density filter.
The intensity detected through each filter is denoted by the vector I. ##EQU4## where I.sub.0 is the intensity passed by the neutral density filter, I.sub.1 is the intensity passed by the 0.degree. polarizer, I.sub.2 is the intensity passed by the 45.degree. polarizer, and I.sub.3 is the intensity passed by the 1/4 wave plate and polarizer. The Stokes' vectors are then defined as EQU S.sub.0 =2I.sub.0 EQU S.sub.1 =2I.sub.1 -2I.sub.0 EQU S.sub.2 =2I.sub.2 -2I.sub.0 EQU S.sub.3 =2I.sub.3 -2I.sub.0
As with the FFT method, all of the polarization vector metrics may be calculated directly from the intensity vector I without necessarily calculating the intermediate Stokes vectors.
A prior art patent, incorporated herein by reference, was issued to a co-inventor, Blair A. Barbour, on Sep. 17, 1996. This patent is U.S. Pat. No. 5,557,261 and is entitled "Ice Monitoring And Detection System" and discloses the use of polarized images to detect the presence and amount of ice on a surface. The system as disclosed in U.S. Pat. No. 5,557,261 uses a rotating polarizer in one embodiment and camera having two different lenses and focal plane arrays in a second embodiment. U.S. Pat. No. 5,557,261 is not concerned with enhancing signals which form the image.